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On the Uniqueness of Isosceles Orthogonality in Normed Linear Spaces

✍ Scribed by Donghai Ji; Jingying Li; Senlin Wu

Publisher
Springer
Year
2010
Tongue
English
Weight
140 KB
Volume
59
Category
Article
ISSN
1422-6383

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## Abstract A triple (__x, y, z__) in a linear 2‐normed space (__X__, β€–.,.β€–) is called an __isosceles orthogonal triple__, denoted |(__x, y, z__), if |(.,.,.) is said to be __homogeneous__ if |(__x, y, z__) implies |(__ax, y, z__) for all real __a__ and it is __additive__ if |(__x~1~__, __y, z__)

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The concept of orthogonality in normed linear spaces has been studied extensively by BIRKHOFF [3], JAMES IS], [7], [8], and the present authors [l], 151, among others. The most natural notion of orthogonality arises in the case where there is an inner product (-, -) compatible with the norm 11. 11 o